Welcome to MathOverflow

Question

2

Let $X_1$, $X_2$, ..., $X_n$ be iid RV's with range $[0,1]$ but unknown distribution. (I'm OK with assuming that the distribution is continuous, etc., if necessary.)

Define $S_n = X_1 + \cdots + X_n$.

I am given $S_k$, and ask: What can I infer, in a Bayesian manner, about $S_n$?

That is, I am given the sum of a sample of size $k$ of the RV's, and I would like to know what I can infer about the distribution of the sum of all the RV's, using a Bayesian approach (and assuming reasonable priors about the distribution).

If the range were $\{0,1\}$ instead of $[0,1]$, then this problem is well-studied, and (with uniform priors) you get (scaled) beta distributions for the inferred distribution on $S_n$. But I'm not sure how to approach it with $[0,1]$ as the range...

edited Mar 8 2012 at 19:25

asked Mar 8 2012 at 14:34

Ronald L Rivest
21●2

Crossposted here: stats.stackexchange.com/questions/24344 – cardinal Mar 8 2012 at 21:02

hsd · Answer 1 · 2012-03-08 18:27:20Z UTC

1

You could try the stats stackexchange. Also you have a typo where you write Sn instead of Xn. This is an answer instead of a comment because I don't have any reputation.

answered Mar 8 2012 at 18:27

hsd
11●1

Thanks; I've reposted this on the stats stackexchange; the problem can be deleted from MO... – Ronald L Rivest Mar 8 2012 at 21:43

Bayesian inference on sum of random variables

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.